1. Field of the Invention
The present invention relates to technology of delay analysis in a circuit.
2. Description of the Related Art
In recent years, with the miniaturization of semiconductor integrated circuits, the influence of statistical variations, e.g., process variations, reductions in power supply voltage, and crosstalk, has become considerable, and circuit delay variations have increased. In conventional static timing analysis (STA), circuit delay variations are accommodated by a larger delay margin; however, timing design becomes difficult due to the larger the delay margin.
Therefore, the need for statistical static timing analysis (SSTA) that can reduce such unnecessary delay margins with accurate consideration statistical variations is increasing. In SSTA, statistical variations include both independent variations and correlated variations between circuit elements/wiring lines.
To accurately obtain a delay distribution of an entire circuit based on SSTA, both types of variations must be considered. The Monte Carlo simulation is an example of a technique for accurately calculating delay distribution over an entire circuit with consideration of such variations.
A technique that separates delay variations relative to opposed paths in an analysis target circuit into systematic variations and random variations, uses the systematic variations and the random variations to approximately calculate the delay distribution of an entire circuit has also been disclosed (see, for example, Japanese Patent Application Laid-open No. 2005-100310).
Further, a technique that sequentially processes paths in an analysis target circuit to approximately calculate the delay distribution of the entire circuit has been disclosed (see, for example, Agarwal, Blaauw, Zolotov, Proc. ICCAD '03, pp. 900-907 (2003)). Specifically, a statistical MAX operation is sequentially performed with respect to a first delay distribution that takes into consideration independent variations between circuit elements/wiring lines of each path and a second delay distribution that takes into consideration correlated variations between circuit elements/wiring lines, and the first delay distribution and the second delay distribution of the entire circuit are calculated. Then, a convolution distribution of the first delay distribution and the second delay distribution of the entire circuit is determined as a delay distribution representing delay in the entire analysis target circuit.
However, according to the conventional Monte Carlo simulation, to calculate the delay distribution with accurate consideration of independent and correlated variations, a huge memory capacity and a long calculation are required. Therefore, the conventional technology has a problem in that the period required for delay analysis is prolonged and the design period is thereby increased.
According to the conventional technology of Japanese Patent Application Laid-open No. 2005-100310, since each statistical variation is estimated as the worst value, a pessimistic and inaccurate delay distribution is calculated. Therefore, circuit design must be consequently adjusted afterwards, resulting in an increased burden on the designer and a longer design period.
According to the conventional technology of Agarwal, Blaauw, Zolotov, Proc. ICCAD '03, pp. 900-907 (2003), when the scale of an analysis target circuit is increased, the number of paths in the analysis target circuit becomes several thousands to several hundred thousands, and the problem of a huge calculation still remains. Consequently, the period required for delay analysis is prolonged and the design period is increased.